Musically there are clear parallels between the two bands in the 60`s. The Stones began to investigate social taboo subjects in their songs by 1965, drugs, sexual frustration, alienation (Paint It Black, Mothers Little Helper, Satisfaction etc) The Velvets then took this idea of bringing "reality" subjects into pop music to an extreme with their first album with songs about taking Heroin and Sado-Masochism (Venus in Furs). As flirters with the dark side I can imagine Mick Jagger was impressed by this record and pushed the envelope even further on with Beggars Banquet (Sympathy with Satanism and Street Fighting Man, away from personal politics into political revolution, even though it seems very dilletant now the Stones were very scary to a generation of parents at the time). Both bands then continued their decadent song content but both became influenced by country rock around 1969 (Let It Bleed and Loaded).Mick Jagger is also the poser/socialite par excellence so he was probably impressed not only by hanging around with Lou Reed, considered at the time as the poet of the underworld but also Andy Warhol the most feted artist of the period. For Lou`s side it was good publicity to be photographed with the biggest rock star in the world, but he never got him into bed unlike Bowie